Who first computed the Euler characteristic of a generalized flag manifold? Let $G$ be a compact Lie group and $H$ a closed subgroup containing a maximal torus $T$ of $G$. Then the Euler characteristic of $G/H$ satisfies $$\chi(G/H) = \frac{|W_G|}{|W_H|},$$ where $W_G = N_G(T)/T$ is the Weyl group of $G$. In particular, $\chi(G/T) = |W_G|$. I want to cite an authority for this very classical result. Who is it most correct (or least wrong) to attribute it to?

According to Diedonne's beautiful history of algebraic topology, Weil first discovered that $\dim H^*(G/T) = |W_G|$, for $T$ a maximal torus of $G$, in 1935, and the result was rediscovered by Hopf-Samelson in 1941. So that answers my question for $H = T$.

Hirsch conjectured a formula which is equivalent, once one knows the relation between the Poincare polynomials of $H^*(G)$ and $H^*(G/T)$, and which was established by Leray in 1949. Although the results are not stated in terms of the Weyl group, this relation appears in Leray's contribution to the 1950 Brussels Colloque de Topologie (Espaces Fibres), so it seems fair to consider it known by then.